I wouldn't think the phaser would be allowed to pick its own target, but that it has a swivel emitter that can be moved by the person holding the gun. If it chose its own target how would it discern friend from foe?
Example, Data and Lore both wearing the same uniform. Neither is armed but in a struggle, they break apart, but only by a foot or less. The one with the phaser has determined which is Lore, but the phaser chooses Data instead.
Swivel emitter good, auto target, not always. Especially in close quarters, or trying to pick off one person out of many.